Magnetic field and accelerated shock acceleration
description
Transcript of Magnetic field and accelerated shock acceleration
Magnetic fieldand
accelerated shock acceleration
Tony Bell
Imperial College, London
Lucek & Bell, MNRAS 314, 65 (2000)Bell & Lucek, MNRAS 321, 433 (2001)Bell, MNRAS 353, 550 (2004)Bell, MNRAS 358,181 (2005)
Reynolds, 1986
SNR suitable CR source below 1015eV
Radio image of SN1006 x-ray image of SN1006
Long, 2003
Cosmic ray wanders around shock-scattered by magnetic field
High velocityplasma
Low velocityplasma
B2
B1
CR track
Due to scattering, CR recrosses shock many times
Cosmic ray wanders around shock-scattered by magnetic field
High velocityplasma
Low velocityplasma
B2
B1
CR track
Due to scattering, CR recrosses shock many times
‘Bohm diffusion’
rg
Mean free path cr ~ rg (proportional to 1/B)
Requires disordered magnetic field: B/B ~ 1
Scaleheight must be less than SNR radius
LR
shock
CR pre-cursor
Need L<R
Bohm diffusion: cr = rg L= rg c /3vshock
Want small rg (large B) for rapid acceleration to high energy
Reducing the CR mean free path
Magnetic field amplification
CR/Alfven wave interaction (conventional theory)
If CR gyration length matches Alfven wavelength
• CR scattered strongly by waves
• Waves excited by CR
B
CR
k in units of rg-1
in units of vS2/crg
For SNR conditions, instability strongly driven- changes nature of turbulence
-4
-2
0
2
4
-2 0 2 4log10(k)
log
10(o
meg
a) Re()
Im()
krg=1
CR interaction with short wavelength waves
CR trajectory
B
CR trajectories unaffected by B
Wave growth driven by jcr||xB
||crj
Electric currents carried by CR and thermal plasma
Density of 1015eV CR: 10-3 m-3
Current density: jcr ~ 10-17 Amp m-2
LR
shock
CR pre-cursorjcr
CR current must be balanced by current carried by thermal plasma
jthermal = - jcr
jthermalxB force acts on plasma to balance jcrxB force on CR
CRcurrent
Current carried by thermal plasma
Magnetic fieldfrozen into
thermal plasma
j x B
j x Bj
j
j x B force expands the spiralLengthens field linesIncreases magnetic fieldIncreases j x B force POSITIVE FEEDBACK (INSTABILITY)
Unstable growth of magnetic field
Time sequence: four adjacent field lines
a)
d)
b)
No reason for non-linear saturation of a single mode
c)
Growth time of fastest growing modeUncertain efficiency factor
SNR expand rapidly for ~1000 yrs
Acceleration favoured by high velocity and high density
Look to very young SNR for high energy
eg SN1993J in M81 (Bartel et al, 2002)
After 1 year: vs =1.5x107 ms-1 ne~106cm-3
After 9 years: vs =0.9x107 ms-1 ne~104cm-3
Shock velocity drops in Sedov phase – reduces max. CR energy
MHD simulations demonstrate
magnetic field amplification
BjBBpt
ucr
||0
)(1
Development of previous modelling, Lucek & Bell (2000)
t=0
t=6.4 t=9.5
t=12.4 t=16.8
0.01
0.1
1
10
100
0 5 10 15
Bperp
Bparallel
Brms
Bmax
Evolution of magnetic field
Magnetic field (log)
time
linear non-linear
rms field grows 30xmax. field grows 100x
3
0
2
~ scrssat vU
c
vB
Estimate of saturationmagnetic field
-4
-2
0
2
4
-2 0 2 4log10(k)
log1
0(gr
owth
rat
e)
Linear growth
kmin kmax
kmin= (CR Larmor radius) -1 ~ B
kmax B = 0 jCR
B increases during non-linear growth
“kmin” increases, “kmax” decreases
Growth saturates when kmax = kmin = 1/CR Larmor radius
3
0
2
vc
v~ scr
ssat UB
Cassiopeia A (Chandra)
Indicates magnetic field amplification at shock
(Vink & Laming, 2003; Völk, Berezhko, Ksenofontov, 2005)
Structure of turbulence
Magnetic field Density
Cavities in density and magnetic field
Slices perpendicular to CR flux at t=6
Field lines – wandering spirals
Cavities and Filaments
Spiral field lines configured as a single mode
Alternative configuration
j x B j x B
Spiral expands leaving a central cavity
Expanding filament
Magnetic field(theta component)
Density
Cavity in density and magnetic field
Filamentation & self-focussing
proton beam jvelocity vbeam
B
MHD response to beam – mean |B| along line of sight
dyB ||
z
xt=2
t=6
t=4
t=8
Current, j
B (0.71,1.32) (0.76,1.17)
Slices of B and in z at t=2
Magnetic field Density
B (0.40,2.61) (0.54,1.59)
Slices of B and in z at t=4
Magnetic field Density
B (0.11,8.53) (0.03,4.13)
Slices of B and in z at t=6
Low density & low B in filament
Magnetic field Density
B (0.,8.59) (0.,4.51)
Slices of B and in z at t=8
Magnetic field Density
Filamentation & self-focussing
proton beam jvelocity vbeam
E=-uxB
B
R
Magnetic field growtht
U
jRR
E
t
B turb
1
~~
Ideal for focussing CR into beam
Focuses CR, evacuates cavity
E=0
E=0
CR exhausts and jets
1) SN in circumstellar wind, aligned rotator
2) CR source at centre of accretion disk
Supernova inWind from star with dipole aligned with rotation axis
CR flux drives cavity along axisLow energy CR escape through cavity
Number of e-foldings ~
c CR pressure CR Larmor radiusvs vs
2 cavity radius
1/2
vs = SNR shock velocity
Accretion disk jets
Central source of CR
Disk wind carries magnetic field
CR flux produces cavity
Exhaust of low energy CR & thermal plasma
Rotating disk threaded by magnetic field
Consequences:• Magnetic field spirals clockwise• Jets on 2 sides or none
Power carried by filament/beam
Natural evolution:1) Beam radius = Larmor radius2) Beam carries Alfven current
00
22
c
BrI eVg
Alfven
Power in individual filament/beam
eVAlfvenAlfven IP W
=1015eV AlfvenP 1.7x1028 W = 3x10-12 Moc2yr-1
=1020eV AlfvenP 1.7x1038 W = 0.03 Moc2yr-1
Black holes: characteristic parameters (Begelman, Blandford & Rees, 1984; based on Eddington luminosity LE)
T
pE
cGMmL
4
2c
GMR
GM
cn
Te
2
2
0
2
2cmn
Bpe
CR energy for which:1) Larmor radius rg = R2) Alfven current carries LE
eV103o
16
2/1
M
M
R
rg
Mass depth independent of black hole mass M2mkg25 RmnR pe
(R for p-p energy loss = 800 kg m-2)
Hillas, 2005
Conclusions
Lucek & Bell, MNRAS 314, 65 (2000)Bell & Lucek, MNRAS 321, 433 (2001)Bell, MNRAS 353, 550 (2004)Bell, MNRAS 358,181 (2005)
• Magnetic field amplification increases max CR energy
• Historical SNR produce CR up to knee
• Very young SNR may get beyond knee
• Exhaust model may connect high energy CR to jets